Question

Consider the two savings plans below. Compare the balances in each plan after 8 years. Which person deposited more money in the plan? Which of the two investment strategies is better?

Yolanda deposits $400 per month in an account with an APR of 3%, while Zach deposits $5000 at the end of each year in an account with an APR of 3.5%.

The balance in Yolanda's saving plan after 8 years was $

The balance in Zach's saving plan after 8 years was $

Which person deposited more money in the plan?

Which of the two investment strategies was better?

Answer 1

Solution

Future value of Annuity=Annuity amount*(((1+r)^n-1)/r)

Where

r=interest rate per period

n=number of periods

For Yolonda

n=8*12=96

r=3/12=.25%

Annuity amount=400

Putting values in formula

Future value of Annuity=400*(((1+.0025)^96-1)/.0025)

=43338.9547 (Amount at end of 8 years)

For Zach

n=8

r=3.5%

Annuity amount=5000

Putting values in formula

Future value of Annuity=5000*(((1+.035)^8-1)/.035)

=45258.43385(Amount at end of 8 years)

Yolonda deposited 400*12*8=38400 in the account while zach deposited 40000 in the account.Thus Zach deposited more money

Now Effective rate for Yolonda= (1+r/12)^12-1=(1+.03/12)^12-1=0.030416=3.0416%

While for Zach the effective rate =3.5%

Thus investment strategy of Zack is better as he earns more intrest

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